Arcturus - Revision history

Sintel: -TempClean

2026-05-28T13:52:30Z

-TempClean

← Older revision		Revision as of 13:52, 28 May 2026
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	~~{{URWTC}}~~
	'''Arcturus''' is the [[non-octave]] [[rank]]-2 [[regular temperament]] of the 3.5.7 [[subgroup]] that [[tempering out\|tempers out]] the arcturus comma, [[15625/15309]]. Having an ~[[5/3]] as a generator, this temperament is the application of the [[Pythagorean]] principle of tuning a stack of the next higher prime number and then factoring out powers of the equivalence to [[tritave]] composition. However, a heptatonic {{mos scalesig\|2L 5s<3/1>\|link=1}} [[MOS]] will not suffice to produce an understandable rendition of it because a very close ~5/3 generates a L:s ratio between 4:1 and 5:1, which is beginning to get too lopsided to still be a complete presentation of a temperament.		'''Arcturus''' is the [[non-octave]] [[rank]]-2 [[regular temperament]] of the 3.5.7 [[subgroup]] that [[tempering out\|tempers out]] the arcturus comma, [[15625/15309]]. Having an ~[[5/3]] as a generator, this temperament is the application of the [[Pythagorean]] principle of tuning a stack of the next higher prime number and then factoring out powers of the equivalence to [[tritave]] composition. However, a heptatonic {{mos scalesig\|2L 5s<3/1>\|link=1}} [[MOS]] will not suffice to produce an understandable rendition of it because a very close ~5/3 generates a L:s ratio between 4:1 and 5:1, which is beginning to get too lopsided to still be a complete presentation of a temperament.

FloraC: Collect non-octave temperaments in one category

2025-04-29T09:19:27Z

Collect non-octave temperaments in one category

← Older revision		Revision as of 09:19, 29 April 2025
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	[[Category:Arcturus\| ]] <!-- main article -->		[[Category:Arcturus\| ]] <!-- main article -->
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]
	[[Category:~~Subgroup temperaments]]~~		[[Category:Non-octave temperaments]]
	~~[[Category:Nonoctave]]~~
	~~[[Category:Tritave~~-~~equivalent~~ temperaments]]

FloraC: - parent category

2025-04-28T13:45:06Z

- parent category

← Older revision		Revision as of 13:45, 28 April 2025
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	* {{mos scalesig\|2L 17s<3/1>\|link=1}} (anti-enharmonic, aka trans-Arcturus 2L 7s)		* {{mos scalesig\|2L 17s<3/1>\|link=1}} (anti-enharmonic, aka trans-Arcturus 2L 7s)

	[[Category:~~Temperaments~~]]		[[Category:Arcturus\| ]] <!-- main article -->
			[[Category:Rank-2 temperaments]]
			[[Category:Subgroup temperaments]]
	[[Category:Nonoctave]]		[[Category:Nonoctave]]
	~~[[Category:Rank-2 temperaments]]~~
	[[Category:Tritave-equivalent temperaments]]		[[Category:Tritave-equivalent temperaments]]

Lériendil at 22:58, 19 April 2025

2025-04-19T22:58:50Z

← Older revision		Revision as of 22:58, 19 April 2025
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	[[Category:Temperaments]]		[[Category:Temperaments]]
	[[Category:Nonoctave]]		[[Category:Nonoctave]]
			[[Category:Rank-2 temperaments]]
	[[Category:Tritave-equivalent temperaments]]		[[Category:Tritave-equivalent temperaments]]

ArrowHead294: /* Scales */

2025-03-08T00:46:27Z

Scales

← Older revision		Revision as of 00:46, 8 March 2025
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	== Scales ==		== Scales ==
	* {{mos scalesig\|9L 2s<3/1>\|link~~=1\|long~~=1}} (mini chromatic, aka sub-Arcturus)		* {{mos scalesig\|9L 2s<3/1>\|link=1}} (mini chromatic, aka sub-Arcturus)
	* {{mos scalesig\|11L 2s<3/1>\|link~~=1\|long~~=1}} (anti-chromatic, aka anti-Arcturus)		* {{mos scalesig\|11L 2s<3/1>\|link=1}} (anti-chromatic, aka anti-Arcturus)
	* {{mos scalesig\|15L 2s<3/1>\|link~~=1\|long~~=1}} (mini enharmonic, aka super-Arcturus 15L 2s)		* {{mos scalesig\|15L 2s<3/1>\|link=1}} (mini enharmonic, aka super-Arcturus 15L 2s)
	* {{mos scalesig\|17L 2s<3/1>\|link~~=1\|long~~=1}} (enharmonic, aka super-Arcturus 17L 2s)		* {{mos scalesig\|17L 2s<3/1>\|link=1}} (enharmonic, aka super-Arcturus 17L 2s)
	* {{mos scalesig\|2L 17s<3/1>\|link~~=1\|long~~=1}} (anti-enharmonic, aka trans-Arcturus 2L 7s)		* {{mos scalesig\|2L 17s<3/1>\|link=1}} (anti-enharmonic, aka trans-Arcturus 2L 7s)

	[[Category:Temperaments]]		[[Category:Temperaments]]
	[[Category:Nonoctave]]		[[Category:Nonoctave]]
	[[Category:Tritave-equivalent temperaments]]		[[Category:Tritave-equivalent temperaments]]

ArrowHead294: /* Scales */ Adopt {{mos scalesig}}

2025-03-08T00:45:52Z

Scales: Adopt {{mos scalesig}}

← Older revision		Revision as of 00:45, 8 March 2025
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	== Scales ==		== Scales ==
	* [[9L~~ ~~2s (3/1~~-equivalent)]]~~ (mini chromatic, aka sub-Arcturus)		* {{mos scalesig\|9L 2s<3/1>\|link=1\|long=1}} (mini chromatic, aka sub-Arcturus)
	* [[11L~~ ~~2s (3/1~~-equivalent)]]~~ (anti-chromatic, aka anti-Arcturus)		* {{mos scalesig\|11L 2s<3/1>\|link=1\|long=1}} (anti-chromatic, aka anti-Arcturus)
	* [[15L~~ ~~2s (3/1~~-equivalent)]]~~ (mini enharmonic, aka super-Arcturus 15L~~ ~~2s)		* {{mos scalesig\|15L 2s<3/1>\|link=1\|long=1}} (mini enharmonic, aka super-Arcturus 15L 2s)
	* [[17L~~ ~~2s (3/1~~-equivalent)]]~~ (enharmonic, aka super-Arcturus 17L~~ ~~2s)		* {{mos scalesig\|17L 2s<3/1>\|link=1\|long=1}} (enharmonic, aka super-Arcturus 17L 2s)
	* [[2L~~ ~~17s (3/1~~-equivalent)]]~~ (anti-enharmonic, aka trans-Arcturus 2L~~ ~~7s)		* {{mos scalesig\|2L 17s<3/1>\|link=1\|long=1}} (anti-enharmonic, aka trans-Arcturus 2L 7s)

	[[Category:Temperaments]]		[[Category:Temperaments]]
	[[Category:Nonoctave]]		[[Category:Nonoctave]]
	[[Category:Tritave-equivalent temperaments]]		[[Category:Tritave-equivalent temperaments]]

ArrowHead294: Replace {{scale link}} with {{mos scalesig}}

2025-03-08T00:32:02Z

Replace {{scale link}} with {{mos scalesig}}

← Older revision		Revision as of 00:32, 8 March 2025
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	{{URWTC}}		{{URWTC}}
	'''Arcturus''' is the [[non-octave]] [[rank]]-2 [[regular temperament]] of the 3.5.7 [[subgroup]] that [[tempering out\|tempers out]] the arcturus comma, [[15625/15309]]. Having an ~[[5/3]] as a generator, this temperament is the application of the [[Pythagorean]] principle of tuning a stack of the next higher prime number and then factoring out powers of the equivalence to [[tritave]] composition. However, a heptatonic {{sl\|2L 5s}} [[MOS]] will not suffice to produce an understandable rendition of it because a very close ~5/3 generates a L:s ratio between 4:1 and 5:1, which is beginning to get too lopsided to still be a complete presentation of a temperament.		'''Arcturus''' is the [[non-octave]] [[rank]]-2 [[regular temperament]] of the 3.5.7 [[subgroup]] that [[tempering out\|tempers out]] the arcturus comma, [[15625/15309]]. Having an ~[[5/3]] as a generator, this temperament is the application of the [[Pythagorean]] principle of tuning a stack of the next higher prime number and then factoring out powers of the equivalence to [[tritave]] composition. However, a heptatonic {{mos scalesig\|2L 5s<3/1>\|link=1}} [[MOS]] will not suffice to produce an understandable rendition of it because a very close ~5/3 generates a L:s ratio between 4:1 and 5:1, which is beginning to get too lopsided to still be a complete presentation of a temperament.

	{{tdlink\|No-twos subgroup temperaments #Arcturus}}		{{tdlink\|No-twos subgroup temperaments #Arcturus}}
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	== Tuning spectrum ==		== Tuning spectrum ==
	Below is a list of MOS families which present it completely (however smearily) using a generator of 845.3 to 951.0 ~~cents~~:		Below is a list of MOS families which present it completely (however smearily) using a generator of 845.3 to 951.0{{c}}:

	{\| class="wikitable" style="text-align: center;"		{\| class="wikitable" style="text-align: center;"

FloraC: Cleanup

2025-01-17T16:59:01Z

Cleanup

Show changes

ArrowHead294 at 14:49, 14 January 2025

2025-01-14T14:49:40Z

← Older revision		Revision as of 14:49, 14 January 2025
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	{{URWTC}}		{{URWTC}}
	'''Arcturus''' is the [[non-octave]] [[rank]]-2 [[regular temperament]] of the 3.5.7 [[subgroup]] that [[tempers out]] the Arcturus comma, [[15625/15309]]. Having an ~[[5/3]] as a generator, this temperament is the application of the [[Pythagorean]] principle of tuning a stack of the next higher prime number and then factoring out powers of the equivalence to [[tritave]] composition. However, a heptatonic [[MOS]] ~~(2L 5s{{angbr\|3/1}})~~ will not suffice to produce an understandable rendition of it because a very close ~5/3 generates a L:s ratio between 4:1 and 5:1, which is beginning to get too lopsided to still be a complete presentation of a temperament.		'''Arcturus''' is the [[non-octave]] [[rank]]-2 [[regular temperament]] of the 3.5.7 [[subgroup]] that [[tempers out]] the Arcturus comma, [[15625/15309]]. Having an ~[[5/3]] as a generator, this temperament is the application of the [[Pythagorean]] principle of tuning a stack of the next higher prime number and then factoring out powers of the equivalence to [[tritave]] composition. However, a heptatonic {{sl\|2L 5s}} [[MOS]] will not suffice to produce an understandable rendition of it because a very close ~5/3 generates a L:s ratio between 4:1 and 5:1, which is beginning to get too lopsided to still be a complete presentation of a temperament.

	{{tdlink\|No-twos subgroup temperaments#Arcturus}}		{{tdlink\|No-twos subgroup temperaments#Arcturus}}
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	\| 84.8005<br />57.962		\| 84.8005<br />57.962
	\| 1768.697<br />1208.917		\| 1768.697<br />1208.917
	\| style="text-align:center;" \|5/3-Pythagorean is near here		\| style="text-align:center;" \| 5/3-Pythagorean is near here
	\|-		\|-
	\|		\|
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	== Scales ==		== Scales ==
	* [[9L 2s (3/1-equivalent)]] (mini chromatic, aka sub-Arcturus)		* [[9L 2s (3/1-equivalent)]] (mini chromatic, aka sub-Arcturus)
	* [[11L 2s (3/1-equivalent)]] (anti-chromatic, aka anti-Arcturus)		* [[11L 2s (3/1-equivalent)]] (anti-chromatic, aka anti-Arcturus)
	* [[15L 2s (3/1-equivalent)]] (mini enharmonic, aka super-Arcturus 15L 2s)		* [[15L 2s (3/1-equivalent)]] (mini enharmonic, aka super-Arcturus 15L 2s)
	* [[17L 2s (3/1-equivalent)]] (enharmonic, aka super-Arcturus 17L 2s)		* [[17L 2s (3/1-equivalent)]] (enharmonic, aka super-Arcturus 17L 2s)
	* [[2L 17s (3/1-equivalent)]] (anti-enharmonic, aka trans-Arcturus 2L 7s)		* [[2L 17s (3/1-equivalent)]] (anti-enharmonic, aka trans-Arcturus 2L 7s)

	[[Category:Temperaments]]		[[Category:Temperaments]]
	[[Category:Nonoctave]]		[[Category:Nonoctave]]
	[[Category:Tritave-equivalent temperaments]]		[[Category:Tritave-equivalent temperaments]]

ArrowHead294: /* Chords */

2025-01-07T13:30:17Z

Chords

← Older revision		Revision as of 13:30, 7 January 2025
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	== Chords ==		== Chords ==
	Arcturus contains the triad 5:7:9 (used in [[~~Bohlen-Pierce~~]] harmony) and the triad 27:35:45 which divides 5/3 into two nearly-equal parts.		Arcturus contains the triad 5:7:9 (used in [[Bohlen–Pierce]] harmony) and the triad 27:35:45 which divides 5/3 into two nearly-equal parts.

	== Tuning spectrum ==		== Tuning spectrum ==